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Liouville Type Results for a p-Laplace Equation with Negative Exponent
by
Zong Ming GUO Lin Feng MEI
in
Applied mathematics
/ Exponents
/ Formulas (mathematics)
/ Inequalities
/ Inequality
/ Laplace transforms
/ Mathematical analysis
/ Mathematical models
/ Mathematics
/ Mathematics and Statistics
/ Operators
/ Partial differential equations
/ Stability
/ Studies
/ Texts
/ Theorems
2016
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Liouville Type Results for a p-Laplace Equation with Negative Exponent
by
Zong Ming GUO Lin Feng MEI
in
Applied mathematics
/ Exponents
/ Formulas (mathematics)
/ Inequalities
/ Inequality
/ Laplace transforms
/ Mathematical analysis
/ Mathematical models
/ Mathematics
/ Mathematics and Statistics
/ Operators
/ Partial differential equations
/ Stability
/ Studies
/ Texts
/ Theorems
2016
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![Liouville Type Results for a p-Laplace Equation with Negative Exponent](https://www.mbrl.ae/o/mbrl-theme/images/site-assets/generic/no-book-image.png)
Liouville Type Results for a p-Laplace Equation with Negative Exponent
by
Zong Ming GUO Lin Feng MEI
in
Applied mathematics
/ Exponents
/ Formulas (mathematics)
/ Inequalities
/ Inequality
/ Laplace transforms
/ Mathematical analysis
/ Mathematical models
/ Mathematics
/ Mathematics and Statistics
/ Operators
/ Partial differential equations
/ Stability
/ Studies
/ Texts
/ Theorems
2016
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Liouville Type Results for a p-Laplace Equation with Negative Exponent
![Liouville Type Results for a p-Laplace Equation with Negative Exponent](https://www.mbrl.ae/o/mbrl-theme/images/site-assets/generic/no-book-image.png)
Journal Article
Liouville Type Results for a p-Laplace Equation with Negative Exponent
2016
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Overview
Positive entire solutions of the equation where 1 〈 p ≤ N, q 〉 0, are classified via their Morse indices. It is seen that there is a critical power q = qc such that this equation has no positive radial entire solution that has finite Morse index when q 〉 qc but it admits a family of stable positive radial entire solutions when 0 〈 q ≤ qc- Proof of the stability of positive radial entire solutions of the equation when 1 〈 p 〈 2 and 0 〈 q ≤ qc relies on Caffarelli-Kohn Nirenberg's inequality. Similar Liouville type result still holds for general positive entire solutions when 2 〈 p ≤ N and q 〉 qc. The case of 1 〈 p 〈 2 is still open. Our main results imply that the structure of positive entire solutions of the equation is similar to that of the equation with p = 2 obtained previously. Some new ideas are introduced to overcome the technical difficulties arising from the p-Laplace operator.
Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society,Springer Nature B.V
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